# Project Ideas

## Prof. James Davenport

This is Prof Davenport's 2003 list of projects. It will be updated with a new list when one is provided. In the meantime, take it as a guide to likely interests.

- An OpenMath-based Unit converter
- OpenMath (http://www.openmath.org/) has a series of "Content Dictionaries". Some of these specify various physical units, such as feet, metres etc., and some conversion factors. The aim is to write a program that takes OpenMath descriptions of physical quantities (e.g. "3 feet") and a target system (e.g. "metric") and do the appropriate conversion, using the Content Dictionaries as the source of information. This would mean that someone could write a new CD, e.g. for U.S. units, and the converter would automatically work on these as well.
- Pre-requisite knowledge: Programming could be in any of several languages, possibly Java.
- Indicative reading: http://www.openmath.org/, notably the standard and the CDs units_metric1, units_imperial1; XML books, e.g. "XML in a nutshell".
- Decompositions of R
^{2n}in RedLog - Davenport et al. (various references to be found on http://staff.bath.ac.uk/masjhd/Simplification)
have suggested that one way to determine reliable simplifications is to
determine the decomposition of C
^{n}(viewed as R^{2n}) induced by the branch cuts of the functions involved. These decompositions can be computed by Cylindrical Algebraic Decomposition (see http://staff.bath.ac.uk/masjhd/TRITA.dvi), though this technique tends to over-decompose R^{2n}, since all that we need is a set of connected components. - The aim of this project is to try the RedLog package on various decompositions coming from Davenport et al. In particular, it is worth seeing how the problem is posed, the order in which the variables are taken (irrelevant for the application, but vital in CAD) etc. affect the running time. The key deliverable will be an informative report with a clear table of examples and times, as well as any conclusions. Ease of formulation in RedLog, and other factors, should also be taken into account.
- This project is also available for supervision by Dr Russell Bradford
- For Maths and Computing students only - preferably MMath.
- Decompositions of R
^{2n}in QEPCAD - Davenport et al. (various references to be found on http://staff.bath.ac.uk/masjhd/Simplification)
have suggested that one way to determine reliable simplifications is to
determine the decomposition of C
^{n}(viewed as R^{2n}) induced by the branch cuts of the functions involved. These decompositions can be computed by Cylindrical Algebraic Decomposition (see http://staff.bath.ac.uk/masjhd/TRITA.dvi), though this technique tends to over-decompose R^{2n}, since all that we need is a set of connected components. - The aim of this project is to try the QEPCAD package on various decompositions coming from Davenport et al. In particular, it is worth seeing how the problem is posed, the order in which the variables are taken (irrelevant for the application, but vital in CAD) etc. affect the running time. The key deliverable will be an informative report with a clear table of examples and times, as well as any conclusions. Ease of formulation in QEPCAD, and other factors, should also be taken into account.
- This project is also available for supervision by Dr Russell Bradford
- Prerequisite Knowledge: Maths and Computing students only - prefereably MMath.
- XML Stores
- There is an "XML store" called Xindice which is part of the Apache project. The aim of the project is to implement this, and load it with XML versions of BiBTeX and Reference Manager files for the University's bibliography. This will need easy-to-use Web pages for updating from people's personal stores. It should use PD tools for importing both BiBTeX and Reference Manager/Endnote databases as XML.
- The AKS Algorithm
- Agrawal et al. (http://www.cse.iitk.ac.in/primality.pdf) have a polynomial-time primality testing algorithm. The aim of the project is to implement this and measure the running times, to come up with an experimental formulation of the runing time, and compare this with the theory.